The dashed triangle is a dilation image

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 298 People

The dashed triangle is a dilation image of the solid triangle with the center at the origin. Is the dilation an enlargement or a reduction? Find the scale factor of the dilation.

Answered by maham237 @ 25/12/2020

Answer:

The dilation is a reduction.

scale factor of the dilation is $\frac{1}{3}$

Step-by-step explanation:

Dilation states that a transformation that changes the size of a figure. It requires a center point and a scale factor (i,e c ).

The value of scale factor c determines whether the dilation is an enlargement or a reduction.

If:

|c| < 1 , then the dilation is a reduction

|c| > 1 , then the dilation is an enlargement.

As you can use any side or even the height of the given triangle to calculate the scale factor.

By using Horizontal height of the given figures:

Height of the original triangle in the solid line is

$6-(-6) = 6+6 =12$

Height of the dilation image in the dashed lines is:

$2-(-2) = 2+2 =4$

Scale factor(c)= $\frac{images height}{original height}$

then;

$c = \frac{4}{12} = \frac{1}{3}$

the, we have $c = \frac{1}{3}< 1$

Therefore, by definition of dilation :

It is a reduction as c < 1

The scale factor of the dilation is; $\frac{1}{3}$

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